1. Field of the Invention
The present invention relates to digital-to-analog converters (DACs), and in particular to an oversampling DAC and to a method for shaping nonlinear intersymbol interference (NLISI) in an oversampling DAC.
2. Related Art
Oversampling DACs are becoming increasingly prevalent due to the favorable position they achieve in the trade-off among bandwidth, dynamic range and implementation complexity. These converters may be broadly classified into discrete-time and continuous-time implementations. The latter are usually favored in high frequency and high bandwidth applications such as the processing of radio and radar signals. See, for example, S. Norsworth, R. Schreier & G. C. Temes (Editors), Delta-Sigma Data Converters, IEEE Press, New Jersey, 1997.
A typical prior art oversampling DAC comprises (i) a digital signal processor that spectrally shapes quantization noise using delta-sigma modulation, (ii) one or more unit-elements that perform the digital-to-analog conversion function, and (iii) an analog filter. The unit elements, together with being components of the overall DAC, are also DACs themselves. The precision of the input to each unit element DAC is one bit. The dynamic range of the overall converter is limited by the characteristics of the individual unit element DACs.
In implementations that use more than one unit element, methods have been used to spectrally shape the mismatch between unit elements in such a way that it does not affect the dynamic range of the overall converter.
For example, FIG. 1 shows an oversampling DAC implemented in accordance with the prior art. The DAC of FIG. 1 comprises: a digital signal processor 1 that spectrally shapes quantization noise using delta-sigma modulation. The digital signal processor 1 comprises: a quantizer 4 that converts a multi-bit digital input signal to a single-bit representation; a first digital filter H1(z) 5 that performs the spectral shaping, i.e. filtering, of the quantizer output; a second digital filter G(z) 6 that performs the spectral shaping of the input signal x[n]; and a summer 7 that combines the filtered input signal with the filtered quantizer output. The oversampling DAC also comprises a unit-element DAC 2 that performs the digital-to-analog conversion function. See, for example, Su and Wooley: “Semi-digital reconstruction filter”, ISSCC 1993, pp. 230-231. The oversampling DAC also comprises an analog filter V(s) 3 that attenuates the out-of-band quantization noise.
For a more detailed explanation of delta-sigma modulation, reference can be made to John G. Proakis, Masoud Salehi: “Communication Systems Engineering”, Prentice Hall 1994, pp. 279-282. More specifically, delta-sigma modulation is a combination of oversampling and feedback, leading to suppression of quantization noise at the low-frequency end of the spectrum. Further prior art details on oversampling DACs can be found in U.S. Pat. No. 6,005,505 and in the references cited therein.
The error mechanism that limits the performance of each of the prior art unit element DACs, and thus the dynamic range of the overall converter, is nonlinear intersymbol interference (NLISI). NLISI arises from nonidealities in the DAC that cause its present output to depend not only on the present sample but also on previous samples of its input.
The primary sources of NLISI are 1) asymmetric rise and fall times in the output waveform, and 2) variation in transition times resulting from the residual effects of prior symbols. NLISI can be accurately represented by the Volterra model, in which the output of the DAC at specified sample times y(nT) is expressed as a function of the present and previous samples of the one-bit quantized signal, u[n], u[n−1], u[n−2], . . . .y(nT)=a·u[n]+b·u[n−1]+c·u[n−2]+d·u[n]·u[n−1]+e·u[n]·u[n−2]+f·u[n−1]·u[n−2]+g·u[n]·u[n−1]·u[n−2]+  (1)where a, b, c, d, e, f and g represent coefficients whose value depends on the specific implementation of the DAC. The first three terms of equation (1) have a linear dependence on the input and do not degrade the performance of the modulator. The additional terms represent nonlinear intersymbol interference (NLISI), which degrades the performance of the modulator. For notational convenience, the two possible values of the one-bit quantized signal u[n] are represented by +1 and −1. A reference expressing NLISI in terms of a Volterra model is, for example, Nonlinear System Theory: The Volterra/Wiener Approach, Johns Hopkins University Press 1981, pp. 253-255.
The simulated output spectrum of a prior art oversampling DAC with NLISI in the unit element is shown by the solid curve of the graph in FIG. 2, which relates to a quiescent input (zero input) case. The horizontal axis of the graph represents frequency and is scaled logarithmically. The vertical axis represents spectral density in decibels. The dashed curve shows, for comparison, what the output spectrum would be in the absence of NLISI. The magnitude of the NLISI in the calculations used to generate FIG. 2 would result from approximately a 1% asymmetry between rise and fall times in the output of the unit element DAC. In this example, NLISI reduces the dynamic range of the converter by approximately 60 dB.
A known method of addressing NLISI makes use of various “return-to-zero” waveforms to increase the spacing between adjacent symbols. For example, nonlinear intersymbol interference caused by asymmetric rise and fall times has been addressed by R. Adams in “A 113 dB SNR oversampling DAC with segmented noise shaped scrambling”, IEEE J. Solid State Circuits, vol. 33 no. 12, pp. 1871-1878 (December 1988). A “dual return-to-zero” scheme is described therein, which generates two data streams from the input data stream. Both data streams represent the same data word, but are offset from each other by half clock cycle. During the opposite half cycle each data stream is returned to zero. Each of the two data streams is applied to a separate digital/analog converter and the results are summed together. This mechanism separates adjacent data words by half cycle within each data stream and thereby reduces NLISI from the adjacent sample.
However, a first disadvantage of the methods using “return-to-zero” waveforms is that they reduce NLISI only insofar as it originates in the immediately preceding symbol and have no effect on longer-term interference. A second disadvantage is that these methods generate high frequency tones in the output spectrum. A further disadvantage is that these methods result in an increased sensitivity to clock jitter. In particular, with reference to the half cycle separation between adjacent data words, this is not sufficient to reduce NLISI to an acceptable level in systems with a very high clock rate. The clock rate used in the prior art is 2.56 MHz, which is very low when compared to the clock rates greater than 1 GHz required in radio and radar applications. Furthermore, the prior art does not provide any correction for the mismatch between the digital/analog subconverters. This mismatch generates a tone that is sufficiently far out-of-band in the example described by the prior art. In other applications, however, the tone generated by mismatch can be problematic.